A short range wireless communication module is provided for an electronic device such as a mobile telephone having a short range wireless communication function. According to specifications, the short range wireless communication module can transition (switch) between a normal mode (non-power-saving mode) and a power-saving mode (low-power consumption mode) that consumes less power than the normal mode. This type of short range wireless communication module transitions from the normal mode to the power-saving mode to suppress the power consumption if a user performs no input operation in the normal mode within a predetermined period (e.g., see patent document 1).    Patent Document 1: JP-A-2003-87359
The power-saving mode consumes less power than the normal mode. However, the power-saving mode processes data more slowly than the normal mode. The short range wireless communication apparatus has the short range wireless communication function. The short range wireless communication module of the communication-party apparatus can transition between the normal mode and the power-saving mode. The short range wireless communication module may issue a request to start data communication in the power-saving mode. In such a case, the short range wireless communication module processes the data communication in the power-saving mode. As a result, the short range wireless communication module slows the data communication process. The data communication rate decreases between the short range wireless communication apparatus and the communication-party apparatus.